Scale limitedness and sampling rate of time limited signals
C. Ramesh, Govind Sharma, P. Rao · 2002
A signal is called scale-limited if the wavelet transform is zero for all scales below a fixed value and for all shifts. The practical considerations due to which this concept has emerged, have been discussed. As an extension the /spl delta//sub 0/ practical scale-limitedness is defined. A signal is called /spl delta//sub 0/-practically scale-limited to a/sub l/ if the fraction of the energy for the scale values less than a/sub l/ and for all shifts is less than /spl delta//sub 0/. Finally it is proved that under reasonable assumptions, for the same error bound on the reconstruction of time-limited signals, the signals with smaller scale-limits should be sampled at a higher rate.